Theory of spin magnetic quadrupole moment and temperature-gradient-induced magnetization

We formulate what we call gravitomagnetoelectric (gravito-ME) effect, in which the magnetization is induced by a temperature gradient. Although the Kubo formula for the gravito-ME effect provides an unphysical divergence at zero temperature, we prove that the correct susceptibility is obtained by subtracting the spin magnetic quadrupole moment from the Kubo formula. It vanishes at zero temperature and is related to the ME susceptibility by the Mott relation. We explicitly calculate the gravito-ME susceptibility in a Rashba ferromagnet and show its experimental feasibility.

[1] A. Shitade, A. Daido, and Y. Yanase, Phys. Rev. B 99, 024404 (2019).